If Tan a + Cot a = 4, Then Tan4 a + Cot4 a is Equal to - Mathematics

Question

If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to

Options

MCQ

Solution

194

We have:

$\tan A + \cot A = 4$

Squaring both the sides:

${(\tan A + \cot A)}^{2} = 4^{2}$

$\Rightarrow \tan^{2} A + \cot^{2} A + 2 (\tan A) (\cot A) = 16$

$\Rightarrow \tan^{2} A + \cot^{2} A + 2 = 16$

$\Rightarrow \tan^{2} A + \cot^{2} A = 14$

Squaring both the sides again:

${(\tan^{2} A + \cot^{2} A)}^{2} = 14^{2}$

$\Rightarrow \tan^{4} A + \cot^{4} A + 2 (\tan^{2} A) (\cot^{2} A) = 196$

$\Rightarrow \tan^{4} A + \cot^{4} A + 2 = 196$

$\Rightarrow \tan^{4} A + \cot^{4} A = 194$

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Trigonometric Equations

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Q 18 Q 17 Q 19

Chapter 5: Trigonometric Functions - Exercise 5.5 [Page 42]

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RD Sharma Mathematics [English] Class 11

Chapter 5 Trigonometric Functions
Exercise 5.5 | Q 18 | Page 42

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